Helppp plzz I will mark brainliestttt

The area of trapezoid $ABCD$ is $\frac{1}{2}h(a+b)$, where $h$ is the height of the trapezoid and $a$ and $b$ are the lengths of the bases $\overline{AB}$ and $\overline{CD}$, respectively.

To find the area of trapezoid $ABCD$, we need to know the lengths of the bases and the height. Let's assume that the lengths of the bases are $a$ and $b$, where $a > b$. The extensions of the legs of the trapezoid intersect at point $P$.

To calculate the area of the trapezoid, we need to find the height. Let's consider triangle $APB$ formed by the extension of the leg $\overline{AB}$, the extension of the leg $\overline{CD}$, and the line segment $\overline{AP}$. Since $\overline{AB}$ and $\overline{CD}$ are parallel, triangle $APB$ is similar to triangle $CPD$.

Using the similarity of triangles, we can set up the following proportion: $\frac{h}{a} = \frac{h+x}{b}$, where $x$ is the length of $\overline{PD}$. Cross-multiplying gives us $bh = ah + ax$. Rearranging the equation, we have $ax = (b-a)h$. Dividing both sides by $a$, we get $x = \frac{b-a}{a}h$.

Now, the height of the trapezoid, $h$, is the sum of the lengths of $\overline{AP}$ and $\overline{PD}$: $h = \overline{AP} + \overline{PD} = x + \frac{b-a}{a}h$. Simplifying the equation, we have $\frac{a}{a}h = x + \frac{b-a}{a}h$, which gives us $\frac{h}{a} = x + \frac{b-a}{a}h$.

Substituting the value of $x$, we have $\frac{h}{a} = \frac{b-a}{a}h + \frac{b-a}{a}h$. Simplifying further, we get $\frac{h}{a} = \frac{2(b-a)}{a}h$. Dividing both sides by $\frac{2(b-a)}{a}$, we find that $h = \frac{a}{2(b-a)}h$.

Finally, we can substitute the value of $h$ in the formula for the area of the trapezoid to find:

$[ABD] = \frac{1}{2}h(a+b) = \frac{1}{2}\left(\frac{a}{2(b-a)}h\right)(a+b) = \frac{a(a+b)}{4(b-a)}$.

The area of trapezoid $ABCD$ with bases $\overline{AB}$ and $\overline{CD}$ is given by $\frac{a(a+b)}{4(b-a)}$, where $a$ and $b$ are the lengths of the bases and $h$ is the height of the trapezoid.

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Answer:

0.14433756

Step-by-step explanation:

sorry if im wrong

Answer:

y = 6

Step-by-step explanation:

Answer:

y = 6

Step-by-step explanation:

y - 8= - (y - 2) / 2

Expand.

y - 8 = (- y + 2) /2

Multiply both sides by 2.

2(y - 8) = - y + 2

2y - 16 = -y + 2

Add y and 16 on both sides.

2y + y = 2 + 16

3y = 18

Divide both sides with 3.

y = 18/3

y = 6

Answer: 15

Step-by-step explanation:

For this question you have to use pythagoras' theorem.

Pythagoras' theorem is c²=a²+b²

So c is the hypotenuse and the hypotenuse is always opposite the right angle.

So the equation would be c²=9²+12²

Then 9²=81 and 12²=144

So the equation would then be c²=81+144

So c²=225

Then you just want to find c on it's own so you have to square root it which is 15.

Answer:

the answer is 4 x 10^4  or 40,000

Step-by-step

the answer is 40,000 but you need to put it in scientific notation which equals 4 x 10 to the 4th power

4 x 10^4

Arlene buys a phone case and charging cord for 15% off

Discount on case and cord = 15%

Original cost of case = $18

Total discount amount = $4.20

Let the original cost of charging cord = x

So, Arlene buys a phone case and charging cord for 15% off = 15% of cost of cord and case

15% of cord and case = 15% of (x + 18)

as the discount amonut ins $18

15% of cord and case = 15% of (x + 18)

15% of cord and case = 4.20

15% of (x + 18) = 4.20

So, the expression is : 15(x + 18) = 420

Simplify the expression for x :

15(x + 18) = 420

15x + 270 = 420

15x = 420 - 270

15x = 150

x = 150/15

x = 10

So, the cost of charging cord is $10

Answer : equation : 15(x + 18) = 420

$10

Answer:

z is greater than or equal to negative three halves

Step-by-step explanation:

subtract 3/4 from each side then simplify.

Answer:

No, Circles never have a side, which makes it always a decimal when trying to find the area of any circle.

No, Σ(an bn) is not necessarily divergent.

The product of two divergent series can converge, as long as their terms cancel each other out to some degree. For example, if an = 1/n and bn = n, then Σan and Σbn are both divergent, but Σ(an bn) = Σ1 is a convergent series.

A series is a convergent (or converges) if the sequence

\({\displaystyle (S_{1},S_{2},S_{3},\dots )}\)of its partial sums tends to a limit; that means that, when adding one

a{k} after the other in the order given by the indices, one gets partial sums that become closer and closer to a given number. More precisely, a series converges, if there exists a number

 such that for every arbitrarily small positive number

there is a (sufficiently large) integer

N such that for all

n>= N,

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Answer:

$3.80

Step-by-step explanation:

380/100= an expected payoff of 3.8 dollars. Hope this helps!

Answer:

3003

Step-by-step explanation:

This is just basically choosing 5 players out of 15 people.

15 choose 5 is \(\frac{15!}{10!*5!}\)

\(\frac{15*14*13*12*11}{5*4*3*2}\)

3*7*13*11=1001*3=3003

Feel free to tell me if I did anything wrong! :)

The basketball team has 3,003,600 possible starting lineups. Given that there are 15 players on the roster and 5 players on the basketball court, this calculation involves determining the number of ways to select 5 players out of the total 15.

To calculate the number of possible starting lineups, we can use the concept of combinations. We have 15 players on the roster, and we need to select 5 players to form a starting lineup.

The number of ways to choose 5 players out of 15 can be calculated using the combination formula:

C(n, r) = n! / (r! * (n - r)!)

In this case, n represents the total number of players (15) and r represents the number of players needed for the lineup (5).

Plugging these values into the formula, we get:

C(15, 5) = 15! / (5! * (15 - 5)!)

= (15 * 14 * 13 * 12 * 11 * 10!) / (5! * 10!)

= (15 * 14 * 13 * 12 * 11) / (5 * 4 * 3 * 2 * 1)

= 3,003,600

Therefore, there are 3,003,600 possible starting lineups for the basketball team. This means that the team has a vast number of combinations to choose from when selecting the starting lineup from the 15 players on its roster.

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Answer:

x = 14

4x = 56

3x - 8 = 34

Step-by-step explanation:

(4x) + (3x -8) = 90

7x + (-8) = 90

7x - 8 = 90

7x (- 8 + 8) = 90 + 8

7x = 98

7x/7 = 98/7

x = 14

4 x 14 = 56

3 x 14 = 42 - 8 = 34

56 + 34 = 90

Answer:

here's your answer

hope it helps

(look at attachment)

The angle of x in the triangle is 75 degrees.

The sum of angles in a triangle is 180 degrees. The triangle is a an isosceles triangle.

An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.

Therefore, the base angles are equal.

The third angle of the triangle is 30 degrees(vertically opposite angles)

Hence,

x + x + 30 = 180

2x + 30 = 180

2x = 180 - 30

2x = 150

x = 150 / 2

x = 75 degrees

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Answer:

C. 2x

Step-by-step explanation:

Let

B's age = x years

A's age = 2 times older than B

= 2 * x

= 2x years

A's age = 2x years

For instance, if B's age is 17 years

Then,

A's age = 2x

= 2(17)

= 34 years old

Answer:

m=-3

Step-by-step explanation:

Since the lines are parallel to each other, their gradients are equal.

∴ gradient of green line = gradient of red line

∴ m = -3

Solution: slope=-3

Detailed explanation:

This little problem asks us to find the slope of the line. Let's do this!

\(\searrow\)

This is what parallel lines look like:

<------------------------------------------------------------------------------------------------------->

<------------------------------------------------------------------------------------------------------->

The two lines above will never intercept each other.

And that's what parallel lines are - they are lines that never intercept.

They can be vertical, horizontal, or diagonal, it doesn't matter. As long as both of them have the same slope and never intercept each other.

So, since parallel lines have identical slopes, the slope of the red line = slope of the green line (the problem provides us that both lines are parallel)

Slope of the red line = -3

Voila! There's our answer!

__________________________

Hope I helped! Best wishes!

Reach far. Aim high. Dream big.

"reflection"

__________________________

Because lines a and b are parallel and lines e and f are parallel, the value of "x" is 82 degrees.

Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance. Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that connect at a straight angle (90 degrees). Parallel lines are lines in a plane that never intersect, no matter how far they are extended. The distance between the parallel lines is continuous since they never intersect.

Here,

Remember that vertical angles are generated by crossing lines that form two non-adjacent angles. These angles are congruent because they have the same vertex.

Take a look at the attached figure. Because lines "a" and "b" are parallel, the angles 82° and x° are vertical angles. As a result, they are congruent.

The value of "x" is 82 degree as lines a and b are parallel and lines e and f are parallel.

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Answer:

0,1,2

Step-by-step explanation:

you have to go in numerical order starting from zero and going forward with no fractions.

a)  The x-intercepts of the graph of f(x) are x = 2.5 and x = -1.

b) The coordinates of the vertex are (0.75, -5.125).

c) By using the x-intercepts and vertex obtained in Parts A and B, we can accurately depict the shape and positioning of the parabolic graph of f(x).

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

Setting f(x) = 0:

\(2x^2 - 3x - 5 = 0\)

To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring is not straightforward, so let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 2, b = -3, and c = -5. Substituting these values into the quadratic formula:

x = (-(-3) ± √((-3)^2 - 4(2)(-5))) / (2(2))

x = (3 ± √(9 + 40)) / 4

x = (3 ± √49) / 4

x = (3 ± 7) / 4

This gives us two possible solutions:

x1 = (3 + 7) / 4 = 10/4 = 2.5

x2 = (3 - 7) / 4 = -4/4 = -1

Therefore, the x-intercepts of the graph of f(x) are x = 2.5 and x = -1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or minimum, we need to consider the coefficient of the x^2 term in the function f(x). In this case, the coefficient is positive (2), which means the parabola opens upward and the vertex represents a minimum point.

To find the coordinates of the vertex, we can use the formula x = -b / (2a). In our equation, a = 2 and b = -3:

x = -(-3) / (2(2))

x = 3 / 4

x = 0.75

To find the corresponding y-coordinate, we substitute x = 0.75 into the function f(x):

f(0.75) = 2(0.75)^2 - 3(0.75) - 5

f(0.75) = 2(0.5625) - 2.25 - 5

f(0.75) = 1.125 - 2.25 - 5

f(0.75) = -5.125

Therefore, the coordinates of the vertex are (0.75, -5.125).

Part C: To graph the function f(x), we can follow these steps:

Plot the x-intercepts obtained in Part A: (2.5, 0) and (-1, 0).

Plot the vertex obtained in Part B: (0.75, -5.125).

Determine if the parabola opens upward (as determined in Part B) and draw a smooth curve passing through the points.

Extend the curve to the left and right of the vertex, ensuring symmetry.

Label the axes and any other relevant points or features.

By using the x-intercepts and vertex obtained in Parts A and B, we can accurately depict the shape and positioning of the parabolic graph of f(x).

The x-intercepts help determine where the graph intersects the x-axis, and the vertex helps establish the lowest point (minimum) of the parabola. The resulting graph should show a U-shaped curve opening upward with the vertex at (0.75, -5.125) and the x-intercepts at (2.5, 0) and (-1, 0).

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Answer:

D: 132 ft

Step-by-step explanation:

C= π2r

So, take pi and multiply that by two..

π2= 6.28

Now, take your radius and multiply it by 6.28.

21 x 6.28= 131.88

Round it two the nearest whole number, which is 132!

Hope this helps!

Answer:

132

Step-by-step explanation:

Answer:

100% of the daily recommended allowance of vitamin C for adults is 80 milligrams.

Step-by-step explanation:

Answer:B.

Step-by-step explanation: I took the same class

Answer:

Step-by-step explanation:

Yes

The partial derivative diffusivity equation for spherical flow is ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t, and for hemispherical flow, it is the same equation.

1. The partial derivative diffusivity equation for spherical flow is derived from the spherical coordinate system and applies to radial flow in a spherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

2. The partial derivative diffusivity equation for hemispherical flow is derived from the hemispherical coordinate system and applies to radial flow in a hemispherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

1. For the derivation of the partial derivative diffusivity equation for spherical flow, we consider a spherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the polar angle (φ). By assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in spherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

2. Similarly, for the derivation of the partial derivative diffusivity equation for hemispherical flow, we consider a hemispherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the elevation angle (ε). Again, assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in hemispherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

In both cases, the term ϕμC/k ∂p/∂t represents the source or sink term, where ϕ is the porosity, μ is the fluid viscosity, C is the compressibility, k is the permeability, and ∂p/∂t is the change in pressure over time.

These equations are commonly used in fluid mechanics and petroleum engineering to describe radial flow behavior in spherical and hemispherical geometries, respectively.

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Answer:

slope is 4 over 7

Step-by-step explanation:

.......

Block diagram representation of R(di/dt) + L(d²i/dt²) + (1/C)i = dV/dt.

The given equation is R(di/dt)+L(d²i/dt²)+(1/C)i = dV/dt.

The block diagram is an essential tool in the analysis and design of dynamic systems. The blocks represent the interconnected subsystems of the system.

The interconnections and external inputs and outputs are shown by the connections between the blocks.The block diagram representation of the equation R(di/dt) + L(d²i/dt²) + (1/C)i = dV/dt is given below.

Therefore, the block diagram representation of the given equation is as follows:

Block diagram representation of R(di/dt) + L(d²i/dt²) + (1/C)i = dV/dt.

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Answer:

Volume of Cuboid = 72 cubic feet

Step-by-step explanation:

Using 1 cubic foot as standard

Given:

Length of given cuboid = 6 feet

Width of given cuboid = 3 foot

Height of given cuboid = 4 foot

Find:

Volume of Cuboid

Computation:

Volume of Cuboid = Length of cuboid x Width of cuboid x Height of cuboid

Volume of Cuboid = (6)(3)(4)

Volume of Cuboid = 72 cubic feet

Answer:

mark brainlest and the answers are in the doc

Factoring means to factor a number means to break it up into numbers that can be multiplied together to get the original number.

To simplify each term by factoring:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.